Bootstrapping the triangles

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Resampling withreplacement- random sampling with replacement from <strong>the</strong>original dataset for b = 1, . . . , B resample fromX 1 , . . . , X n with replacement and obtain X ∗ 1,b , . . . , X∗ n,b
Bootstrap example- input data (# of catastrophic claims per year in 10yhistory): 35, 34, 13, 33, 27, 30, 19, 31, 10, 33 mean = 26.5, sd = 9.168182Case sampling◮.◮bootstrap sample 1 (1st draw with replacement):30, 27, 35, 35, 13, 35, 33, 34, 35, 33 mean ∗ 1 = 31.0, sd ∗ 1 = 6.847546bootstrap sample 1000 (1000th draw withreplacement): 19, 19, 31, 19, 33, 34, 31, 34, 34, 10 mean ∗ 1000 = 26.4, sd ∗ 1000 = 8.771165- mean ∗ 1 , . . . , mean∗ 1000 provide bootstrap empiricaldistribution for mean and sd ∗ 1 , . . . , sd∗ 1000 providebootstrap empirical distribution for sd (REALLY!?)
Page 1 and 2: Bootstrapping the trianglesPrečo,
Page 3 and 4: Prologue forBootstrap- computationa
Page 5: Bootstrap- simple (distribution-ind
Page 9 and 10: Run-off (incremental)triangleAccide
Page 11 and 12: Run-off (cumulative)triangleAcciden
Page 14 and 15: Raw residuals(R)r i,j = X i,j −
Page 16 and 17: Anscombe residuals I- in GLM or GEE
Page 18 and 19: Deviance residuals(D)r i,j = sign(X
Page 20 and 21: Adjusted residuals- alternative to
Page 22 and 23: Bootstrap procedure I- Ex: bootstra
Page 24 and 25: Bootstrap procedure III(7) calculat
Page 26 and 27: Development of claimsClaims1e+06 3e
Page 28 and 29: Chain ladder diagnosticsValue0e+00
Page 30 and 31: Mack CL vs bootstrapGLM (ODP)Accide
Page 32 and 33: Conclusions- mean and variance do n
Page 34: Thank you !pesta@karlin.mff.cuni.cz

Bootstrapping the triangles

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